You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Mathematics

Theorems for Differentiability

The law of th...

Question

The law of the mean can also be put in the form

f (a + h) = f (a) - h f^{'} (a + q h)

0 < q < 1

No worries! We‘ve got your back. Try BYJU‘S free classes today!

f (a + h) = f (a) + h f^{'} (a + q h)

0 < q < 1

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

f (a + h) = f (a) + h f^{'} (a - q h)

0 < q < 1

No worries! We‘ve got your back. Try BYJU‘S free classes today!

f (a + h) = f (a) - h f^{'} (a - q h)

0 < q < 1

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is D $f (a + h) = f (a) + h f^{'} (a + q h)$ $0 < q < 1$
The law of mean is $f^{1} (a + q h) = \frac{f (a + h) - f (a)}{h}$ , where $0 < q < 1$
It can be put in the form of $f (a + h) = f (a) + h f^{'} (a + q h)$ , where $0 < q < 1$
Therefore the correct option is $B$

Suggest Corrections

Similar questions

A function f(x) is called as a strictly increasing function about a point ‘a’ If -

Where 'h' is a positive real number tending to zero.

Q. If

f (x)

is a continuous function defined on

[a, b]

such that

f (x) \geq 0

x \in [a, b]

then the area under the curve as the limit of a sum can be given as

(b - a) lim n \to \infty \frac{1}{n} [f (a) + f (a + h) . . . f (a + (n - 1) h)]

Where

h = \frac{b - a}{n}

and

h \to 0

n \to \infty

Left hand derivative and right hand derivative of a function

f (x)

at a point

x = a

are defined as

f^{'} (a^{-}) = lim h \to 0^{+} \frac{f (a) - f (a - h)}{h} = lim h \to 0^{-} \frac{f (a) - f (a - h)}{h} = lim x \to a^{+} \frac{f (a) - f (x)}{a - x}

respectively

Let

f

be a twice differentiable function. We also know that derivative of an even function is odd function and derivative of an odd function is even function.

The statement

lim h \to 0 \frac{f (- x) - f (- x - h)}{h} = lim h \to 0 \frac{f (x) - f (x - h)}{- h}

implies that for all x

ϵ R

Left hand derivative and right hand derivative of a function

f (x)

at a point

x = a

are defined as

f^{'} (a^{-}) = lim h \to 0^{+} \frac{f (a) - f (a - h)}{h} = lim h \to 0^{-} \frac{f (a) - f (a - h)}{h} = lim x \to a^{+} \frac{f (a) - f (x)}{a - x}

respectively

Let

f

be a twice differentiable function. We also know that derivative of an even function is odd function and derivative of an odd function is even function.

f

is odd, which of the following is Left-hand derivative of

f

x = a

Left hand derivative and right hand derivative of a function

f (x)

at a point

x = a

are defined as

f^{'} (a^{-}) = lim h \to 0^{+} \frac{f (a) - f (a - h)}{h} = lim h \to 0^{-} \frac{f (a) - f (a - h)}{h} = lim x \to a^{+} \frac{f (a) - f (x)}{a - x}

respectively

Let

f

be a twice differentiable function. We also know that derivative of an even function is odd function and derivative of an odd function is even function.

f

is even, which of the following is Right hand derivative of

f^{'}

x = a

Join BYJU'S Learning Program

The law of the mean can also be put in the form

The correct option is D f(a+h)=f(a)+hf′(a+qh) 0<q<1The law of mean is f1(a+qh)=f(a+h)−f(a)h , where 0<q<1It can be put in the form of f(a+h)=f(a)+hf′(a+qh) , where 0<q<1Therefore the correct option is B

The correct option is D $f (a + h) = f (a) + h f^{'} (a + q h)$ $0 < q < 1$
The law of mean is $f^{1} (a + q h) = \frac{f (a + h) - f (a)}{h}$ , where $0 < q < 1$
It can be put in the form of $f (a + h) = f (a) + h f^{'} (a + q h)$ , where $0 < q < 1$
Therefore the correct option is $B$